kc3-lang/SDL/src/libm/e_log.c

• Show log

  Commit

• Hash : f848adff
  Author :
  Date : 2013-11-29T10:06:08
  

  Improve Android pause/resume behavior.

Download

• src/libm/e_log.c

• /* @(#)e_log.c 5.1 93/09/24 */
  /*
   * ====================================================
   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   *
   * Developed at SunPro, a Sun Microsystems, Inc. business.
   * Permission to use, copy, modify, and distribute this
   * software is freely granted, provided that this notice
   * is preserved.
   * ====================================================
   */
  
  #if defined(LIBM_SCCS) && !defined(lint)
  static const char rcsid[] =
      "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $";
  #endif
  
  /* __ieee754_log(x)
   * Return the logrithm of x
   *
   * Method :
   *   1. Argument Reduction: find k and f such that
   *			x = 2^k * (1+f),
   *	   where  sqrt(2)/2 < 1+f < sqrt(2) .
   *
   *   2. Approximation of log(1+f).
   *	Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
   *		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
   *	     	 = 2s + s*R
   *      We use a special Reme algorithm on [0,0.1716] to generate
   * 	a polynomial of degree 14 to approximate R The maximum error
   *	of this polynomial approximation is bounded by 2**-58.45. In
   *	other words,
   *		        2      4      6      8      10      12      14
   *	    R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s  +Lg6*s  +Lg7*s
   *  	(the values of Lg1 to Lg7 are listed in the program)
   *	and
   *	    |      2          14          |     -58.45
   *	    | Lg1*s +...+Lg7*s    -  R(z) | <= 2
   *	    |                             |
   *	Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
   *	In order to guarantee error in log below 1ulp, we compute log
   *	by
   *		log(1+f) = f - s*(f - R)	(if f is not too large)
   *		log(1+f) = f - (hfsq - s*(hfsq+R)).	(better accuracy)
   *
   *	3. Finally,  log(x) = k*ln2 + log(1+f).
   *			    = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
   *	   Here ln2 is split into two floating point number:
   *			ln2_hi + ln2_lo,
   *	   where n*ln2_hi is always exact for |n| < 2000.
   *
   * Special cases:
   *	log(x) is NaN with signal if x < 0 (including -INF) ;
   *	log(+INF) is +INF; log(0) is -INF with signal;
   *	log(NaN) is that NaN with no signal.
   *
   * Accuracy:
   *	according to an error analysis, the error is always less than
   *	1 ulp (unit in the last place).
   *
   * Constants:
   * The hexadecimal values are the intended ones for the following
   * constants. The decimal values may be used, provided that the
   * compiler will convert from decimal to binary accurately enough
   * to produce the hexadecimal values shown.
   */
  
  #include "math_libm.h"
  #include "math_private.h"
  
  #ifdef __STDC__
  static const double
  #else
  static double
  #endif
    ln2_hi = 6.93147180369123816490e-01,  /* 3fe62e42 fee00000 */
      ln2_lo = 1.90821492927058770002e-10,        /* 3dea39ef 35793c76 */
      two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
      Lg1 = 6.666666666666735130e-01,     /* 3FE55555 55555593 */
      Lg2 = 3.999999999940941908e-01,     /* 3FD99999 9997FA04 */
      Lg3 = 2.857142874366239149e-01,     /* 3FD24924 94229359 */
      Lg4 = 2.222219843214978396e-01,     /* 3FCC71C5 1D8E78AF */
      Lg5 = 1.818357216161805012e-01,     /* 3FC74664 96CB03DE */
      Lg6 = 1.531383769920937332e-01,     /* 3FC39A09 D078C69F */
      Lg7 = 1.479819860511658591e-01;     /* 3FC2F112 DF3E5244 */
  
  #ifdef __STDC__
  static const double zero = 0.0;
  #else
  static double zero = 0.0;
  #endif
  
  #ifdef __STDC__
  double attribute_hidden
  __ieee754_log(double x)
  #else
  double attribute_hidden
  __ieee754_log(x)
       double x;
  #endif
  {
      double hfsq, f, s, z, R, w, t1, t2, dk;
      int32_t k, hx, i, j;
      u_int32_t lx;
  
      EXTRACT_WORDS(hx, lx, x);
  
      k = 0;
      if (hx < 0x00100000) {      /* x < 2**-1022  */
          if (((hx & 0x7fffffff) | lx) == 0)
              return -two54 / zero;       /* log(+-0)=-inf */
          if (hx < 0)
              return (x - x) / zero;      /* log(-#) = NaN */
          k -= 54;
          x *= two54;             /* subnormal number, scale up x */
          GET_HIGH_WORD(hx, x);
      }
      if (hx >= 0x7ff00000)
          return x + x;
      k += (hx >> 20) - 1023;
      hx &= 0x000fffff;
      i = (hx + 0x95f64) & 0x100000;
      SET_HIGH_WORD(x, hx | (i ^ 0x3ff00000));    /* normalize x or x/2 */
      k += (i >> 20);
      f = x - 1.0;
      if ((0x000fffff & (2 + hx)) < 3) {  /* |f| < 2**-20 */
          if (f == zero) {
              if (k == 0)
                  return zero;
              else {
                  dk = (double) k;
                  return dk * ln2_hi + dk * ln2_lo;
              }
          }
          R = f * f * (0.5 - 0.33333333333333333 * f);
          if (k == 0)
              return f - R;
          else {
              dk = (double) k;
              return dk * ln2_hi - ((R - dk * ln2_lo) - f);
          }
      }
      s = f / (2.0 + f);
      dk = (double) k;
      z = s * s;
      i = hx - 0x6147a;
      w = z * z;
      j = 0x6b851 - hx;
      t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
      t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
      i |= j;
      R = t2 + t1;
      if (i > 0) {
          hfsq = 0.5 * f * f;
          if (k == 0)
              return f - (hfsq - s * (hfsq + R));
          else
              return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) -
                                    f);
      } else {
          if (k == 0)
              return f - s * (f - R);
          else
              return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f);
      }
  }
  

Download